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partial derivative of 5xy-7x^2-y^2+3x-6y+2
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∂
∂
x
(
5
xy
−
7
x
2
−
y
2
+
3
x
−
6
y
+
2
)
=
5
y
+
3
−
1
4
x
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∂
∂
x
(
5
xy
−
7
x
2
−
y
2
+
3
x
−
6
y
+
2
)
=
5
y
+
3
−
1
4
x
steps
∂
∂
x
(
5
xy
−
7
x
2
−
y
2
+
3
x
−
6
y
+
2
)
Treat
y
as
a
constant
Apply
the
Sum
/
Difference
Rule
:
(
f
±
g
)
′
=
f
′
±
g
′
=
∂
∂
x
(
5
xy
)
−
∂
∂
x
(
7
x
2
)
−
∂
∂
x
(
y
2
)
+
∂
∂
x
(
3
x
)
−
∂
∂
x
(
6
y
)
+
∂
∂
x
(
2
)
show steps
∂
∂
x
(
5
xy
)
=
5
y
show steps
∂
∂
x
(
7
x
2
)
=
1
4
x
show steps
∂
∂
x
(
y
2
)
=
0
show steps
∂
∂
x
(
3
x
)
=
3
show steps
∂
∂
x
(
6
y
)
=
0
show steps
∂
∂
x
(
2
)
=
0
=
5
y
−
1
4
x
−
0
+
3
−
0
+
0
Simplify
=
5
y
+
3
−
1
4
x
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